Related papers: Spin-statistics relation for quantum Hall states
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…
The electron-electron interaction in the Landau levels of bilayer graphene is markedly different from that of conventional semiconductors such as GaAs. We show that in the zeroth Landau level of bilayer graphene, in the orbital which is…
A nonrelativistic proof of the spin-statistics theorem is given in terms of the field operators satisfying commutation and anticommutation relations, which are introduced here in the coordinate space as a means to build the permutation…
We propose an experimentally-feasible system based on spin transitions in the fractional quantum Hall effect regime where parafermions, high-order non-abelian excitations, can be potentially realized. We provide a proof-of-concept…
Effects of electron correlations on a two dimensional quantum spin Hall (QSH) system are studied. We examine possible phases of a generalized Hubbard model on a bilayer honeycomb lattice with a spin-orbit coupling and short range…
While the values for the fractional charge and fractional statistics coincide for fractional Hall (FQH) states in the Laughlin sequence, they do not for more general FQH states, such as those in the Jain sequence. This mismatch leads to…
We discuss the relationship between fractional quantum Hall (FQH) states at filling factor $\nu=p/(2p+1)$ and quantum spin chains. This series corresponds to the Jain series $\nu=p/(2mp+1)$ with $m=1$ where the composite fermion picture is…
The energy and photoluminescence spectra of a two-dimensional electron gas in the fractional quantum Hall regime are studied. The single-particle properties of reversed-spin quasielectrons (QE$_{\rm R}$'s) as well as the pseudopotentials of…
A large class of fractional quantum Hall (FQH) states can be classified according to their pattern of zeros, which describes the order of zeros in ground state wave functions as various clusters of electrons are brought together. The…
Strong interaction between electrons in two-dimensional systems in the presence of a high magnetic field gives rise to fractional quantum Hall states that host quasiparticles with fractional charge and fractional exchange statistics. Here,…
The calculation of pair correlations and density profiles of quasiholes are routine steps in the study of proposed fractional quantum Hall states. Nevertheless, the field has not adopted a standard way to present the results of such…
We show that electronic materials with disallowed rotational symmetries that enforce quasiperiodic order can exhibit quantum oscillations and that these are generically associated with exotic "spiral Fermi surfaces." These Fermi surfaces…
We provide a detailed description of a new symmetry structure of the monomial (Slater) expansion coefficients of bosonic (fermionic) fractional quantum Hall states first obtained in Ref. 1, which we now extend to spin-singlet states. We…
We theoretically consider coherence times for spins in two quantum computer architectures, where the qubit is the spin of an electron bound to a P donor impurity in Si or within a GaAs quantum dot. We show that low temperature decoherence…
Since the ground-breaking discovery of the quantum Hall effect, half-quantized quantum Hall plateaus have been some of the most studied and sought-after states. Their importance stems not only from the fact that they transcend the composite…
Despite the rapid progresses in the field of quantum spin Hall (QSH) effect, most of the QSH systems studied up to now are based on crystalline materials. Here we propose that the QSH effect can be realized in quasicrystal lattices (QLs).…
We construct the hierarchical wave function of the spin-singlet fractional quantum Hall effect, which turns out to satisfy Fock cyclic condition. The spin-statistics relation of the quasi-particles in the spin-singlet fractional quantum…
We numerically study the behavior of spin--$1/2$ fermions on a two-dimensional square lattice subject to a uniform magnetic field, where opposite spins interact via an on-site attractive interaction. Starting from the non-interacting case…
Starting from the Pauli Hamiltonian operator, we derive a scalar quantum kinetic equations for spin-1/2 systems. Here the regular Wigner two-state matrix is replaced by a scalar distribution function in extended phase space. Apart from…
Interference of fractionally charged quasi-particles is expected to lead to Aharonov-Bohm oscillations with periods larger than the flux quantum. However, according to the Byers-Yang theorem, observables of an electronic system are…